Modeling of adaptive bone remodeling and its application to optimal design of structure/material system (Approach to multilevel structural system)

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An orthogonal lattice continuum is studied as a model of trabecular architecture of cancellous bone and the relation between parameters of lattice geometry and mechanical characteristics as a continuum is considered in the context of unit cell analysis. A rate equation of orthogonal lattice parameters is described for a phenomenological model of adaptation by bone remodeling by paying attention to some optimality in mechanical function at equilibrium. The lattice continuum model is extended to permit the non-orthogonal lattice intersection, and the lattice parameter determination is considered. The residual stress in trabecular architecture is observed and estimated based on a lattice model.As an application of cancellous bone-like internal structure to a structural design problem, a topology and shape determination problem is formulated for a variable stiffness structure that realize different stiffness at different level of external load, and a solution procedure is demonstrated. This problem is extended for a design of a material structural system with specified elastic material constants depending on working load level.